Bypass Gate-to-trigger-converter via switching jack

Goal

I like to trigger a LF398 Sample-and-Hold IC via a 3.5mm Jack (modular synthesizer). The desired behaviour would be:

1. if a cable is plugged in, incoming signals will be converted to short triggers.
2. if no cable is plugged in, the LF398 should sample all the time (the trigger part should be essentially bypassed)

This is the way the circuit looks right now:

The sections of the circuit are described below. The simulation pictured can be found here.

Problem

Is there any way I can reach the goal without adding too many parts or increasing complexity? Can I switch a signal path just by this switching jack?

Maybe if I exchange the switching jack with a stereo jack and add something on the ring that switches high as it is pulled to ground?

Edit: lifting ground at D8 and R20 would work, but how do I switch it the way I want?